Roasted/baked potatoes and yams on the grill are very good. Just wash and put on the grill whole, preferably under coals or low flames; the skins will get crispy, but the innards will be tasty. I like root vegetables baked/roasted whole, so rutabagas, turnips, beets and parsnips ought to be good. Stir-fried carrots are good, so I bet roasted/grilled whole carrots would be mighty fine, too. Basically veggie that is big enough not to fall through the grill bars ought to be yummy. Sliced-long-way squash ought to be good too (these I'd brush with olive oil and herbs).

As for the person recommending quartered head of romaine grilled, seems like there would be a whole lot of wilting going on there.

Oh and corn on the cob-just carefully peel back husk, remove silk and fold back husk. Some soak in water but I just hold under the faucet until wet and then put on the grill. It is so very good and can lift so so corn and with good corn it is just the best thing ever.